Counting Terms

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When the Chef is not busy with cooking delicious foods, one of his favorite pastime is to solve mathematical problem. But as you know, he is not very good with programming. So when he fails to solve a problem he usually asks John to write a program that will solve it.

Recently the chef became interested in finding the expansion of (x1+x2+....+xk)n. Specifically he is more interested in number of terms in it. Being unable to solve the problem he asked John for help. The conversation between John and chef goes as

Chef: Can you write a program that will calculate f(n,k)= number of terms in (x1+x2+....+xk)n ?

John: That is a very easy problem.

Chef: Oh, really? Then calculate the sum over (i=0 to n) (f(i,k))

John: That is also an easy problem.

Chef: Then go finish it. And did I mention that I am calculating modulo a prime number p.

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